Learn about what a beam is and what 7 different types of beams are used (2 examples: simply supported and cantilever beam)

As it appears at any point of the beam, we cut the beam. This is done to calculate the internal forces, such as bending moments. We have already written a more detailed article about the internal force calculation.

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Cantilever beam: Quick overview of the bending moment and shear force formulas for beams due to different loading scenarios.

Uniform load formula

So the moment M in a specific point of a beam element is calculated by a force $\cdot$ lever arm. The lever arm is the parallel distance to the point.

In most cases, we have more than 1 load that need to be considered in the bending moment. So let’s look at the example from above, where we applied a line load and cut the beam.

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In easier words, a bending moment refers to the tendency of a structural element to deform due to external loading (self-weight, snow, wind, people etc.).

Alright, if you googled how to calculate a bending moment, you probably don’t know what a force or a lever arm is. Let’s explain it with a figure. 🖼️🖼️

Shear andmomentdiagram sign convention

Due to this bending moment, the beam experiences compression in the top part and tension in the bottom part. The point along the beam where the bending moment is zero is called the neutral axis.

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Typical bendingmomentdiagrams

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In the picture, you can also see that the biggest stresses – compression and tension – appear in the most outer fibres of the beam.

I hope that this article helped you understand the bending moment better and how to go further from here. In case you still have questions.

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Momentload formula

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Quick overview of the bending moment and shear force formulas for simply supported beams due to different loading scenarios.

Yes, there are many structural engineering software programs that can calculate the bending moments. For example: Dlubal RFEM, Autodesk Robot, Ftool, Polybeam, SOFiSTiK, FEM Design and many more.

For the most used static systems, there are luckily formulas that help us to calculate the bending moments. We covered them extensively in the following articles:

We use moment equilibrium in point b to calculate Av, because the support in point b is a hinge and therefore the moment = 0.

Now, that you got an understanding of bending moments, you can learn about how to use the bending moment to design structural elements such as

Momentsign convention

The timber beams that you can see in the picture above are calculated as a simply supported beam. External loads like snow, dead and wind load are applied to the beam and the bending moment is calculated to dimension the size of the timber beams.

The steel beams in the picture above carry the loads of the timber beams. Due to those loads, the steel beams are subjected to bending moments which need to be resisted. We show in our steel beam design guide how to verify the bending moments.

The King Post Truss is a structural system commonly used as a roof structure. But what are its different members, and how does it work? Learn more in this article.

Area method shear andmomentdiagram

A great visualization of the calculated results is a bending moment diagram. The following diagram visualizes the bending moments of the example above.

A bending moment describes the internal force that leads to bending of a structural element such as a beam due to loading.

Momentload on beam

The bending moment at any point along a structural element can be calculated by multiplying the force applied to the beam by the perpendicular distance from the point of interest to the line of action of the force. The unit is kilonewton-meters (kNm) in Europe and foot-points (ft-lb) in the US.

Momentof a triangular distributed load

Moments can be calculated at any location of a beam. If the beam is 5 m long, then we could have calculated the moment also with a lever arm of 3.1 m or 4.5 m.

Second, we do moment equilibrium, which means that all moments in point x need to equal 0. Again, a moment is calculated by a point load $\cdot$ lever arm.

The rafters of the roof are exposed to the external loads such as wind, snow and dead load. This leads to bending moments in the rafters, and the bending capacity of the timber beams need to be bigger than the bending moments.

A bending moment describes the internal force or moment that causes a beam, column, or any structural element to bend. If the moment resistance of a structural element is smaller than the bending moment that acts in an element, the structure will fail.

2 span continuous beam: Quick overview of the bending moment, shear and reaction force formulas for beams due to different loading scenarios.

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